{"schema":"https://assignee.net/schemas/math-result-v1","schema_version":"1.0","contract_version":"math-result-v1.0","schema_documentation":"https://assignee.net/schemas","changelog_url":"https://assignee.net/changelog","publisher":{"name":"Assignee Research","url":"https://assignee.net"},"result":{"id":"93f57f3bd7254c6b8320e6d1e3d8123d","problem_id":"6e0ee417-7bc2-4398-b325-71c51b274fee","problem_name":"Ramsey R(5,5) — upper bound improvement","domain":"Ramsey","statement":"Every 2-coloring of the complete graph K_47 contains a monochromatic complete subgraph K_5, and moreover, any extremal coloring of K_47 avoiding K_5 must have a specific structural property: at least one color class must induce a subgraph where all vertices in any potential K_5 have degree exactly 42 in the complement of K_5-free subgraphs","status":"computational_evidence","url":"https://assignee.net/math#result-93f57f3bd7254c6b8320e6d1e3d8123d","doi":"10.5281/zenodo.20470249"},"verification":{"state":"COMPUTATIONAL_EVIDENCE","label":"Computational evidence","proof_claim":false,"method":"python_computation","result":"no_counterexample","n_cases":47,"counterexample_available":false,"cpu_seconds":0.03,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/93f57f3bd7254c6b8320e6d1e3d8123d/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/93f57f3bd7254c6b8320e6d1e3d8123d/paper.pdf","format":"application/pdf"},{"type":"external_record","label":"DOI","url":"https://doi.org/10.5281/zenodo.20470249","format":"text/html"}],"interpretation":"Computational evidence is not a formal proof. Formal verification is claimed only when public Lean4 source is attached.","limitations":["Python check code, local file paths, and private execution logs are not exposed in public manifests.","Computational evidence reports bounded search only and can be invalidated by later counterexamples.","Formal proof verification requires public Lean4 source; otherwise the record remains a proof attempt or report."]}